I have done that for a couple of my sites. It helped them rank better and it also gave me a PR boost. I really focus on the top sites and work my way down the list. However, I do not go for low quality sites, or sites with tons of OBL etc.
Besides finding relevant places on my own to drop a link, I am also watching what the competitors have done and see if I can drop a link at the same place if the site is relevant.
Is it correct to start with backlinks to the competitor site that ranks first and then just work down to competitor backlinks from subsequent search results (worse rankings)?
Do you consider backlinks of sites that appear at second and subsequent pages too initially? Or, does it really matter at all?
I try to get links at the same places as my competitors. For one of my sites, I found the site that ranks #1 for my keywords and bought advertisements all over it